#!/usr/bin/env python3
"""
UBP Mathematical Framework Implementation
Core computational components for Universal Binary Principle

This module implements the fundamental mathematical structures and operations
defined in the UBP framework, providing the computational foundation for
Millennium Prize Problem solutions.
"""

import numpy as np
import scipy.sparse as sp
from typing import Tuple, List, Dict, Optional, Union
from dataclasses import dataclass
from enum import Enum
import math

class ToggleOperation(Enum):
    """Enumeration of toggle algebra operations"""
    AND = "and"
    XOR = "xor" 
    OR = "or"
    RESONANCE = "resonance"
    ENTANGLEMENT = "entanglement"
    SUPERPOSITION = "superposition"

class BitfieldLayer(Enum):
    """OffBit Ontology layers"""
    REALITY = (0, 5)      # bits 0-5: physical phenomena
    INFORMATION = (6, 11)  # bits 6-11: data processing
    ACTIVATION = (12, 17)  # bits 12-17: energy states
    UNACTIVATED = (18, 23) # bits 18-23: potential states

@dataclass
class OffBit:
    """
    Fundamental 24-bit unit of UBP reality model
    
    Attributes:
        bits: 24-bit binary vector representing the OffBit state
        position: 6D coordinates in the Bitfield
        layer_mask: Active layers for this OffBit
    """
    bits: np.ndarray  # shape (24,) dtype bool
    position: Tuple[int, int, int, int, int, int]
    layer_mask: int = 0b111111  # all layers active by default
    
    def __post_init__(self):
        if self.bits.shape != (24,):
            raise ValueError("OffBit must have exactly 24 bits")
        if not np.issubdtype(self.bits.dtype, np.bool_):
            self.bits = self.bits.astype(bool)
    
    def get_layer(self, layer: BitfieldLayer) -> np.ndarray:
        """Extract bits from specific layer"""
        start, end = layer.value
        return self.bits[start:end+1]
    
    def set_layer(self, layer: BitfieldLayer, values: np.ndarray):
        """Set bits in specific layer"""
        start, end = layer.value
        if values.shape != (end - start + 1,):
            raise ValueError(f"Layer {layer.name} requires {end-start+1} bits")
        self.bits[start:end+1] = values

class ToggleAlgebra:
    """Implementation of UBP toggle algebra operations"""
    
    @staticmethod
    def and_op(b1: OffBit, b2: OffBit) -> OffBit:
        """AND operation: min(b1, b2) - crystalline structures"""
        result_bits = np.minimum(b1.bits, b2.bits)
        return OffBit(result_bits, b1.position)
    
    @staticmethod
    def xor_op(b1: OffBit, b2: OffBit) -> OffBit:
        """XOR operation: |b1 - b2| - neural networks"""
        result_bits = np.abs(b1.bits.astype(int) - b2.bits.astype(int)).astype(bool)
        return OffBit(result_bits, b1.position)
    
    @staticmethod
    def or_op(b1: OffBit, b2: OffBit) -> OffBit:
        """OR operation: max(b1, b2) - quantum superposition"""
        result_bits = np.maximum(b1.bits, b2.bits)
        return OffBit(result_bits, b1.position)
    
    @staticmethod
    def resonance_op(offbit: OffBit, frequency: float, distance: float = 0.0) -> OffBit:
        """
        Resonance operation: b * f(d) where f(d) = exp(-k*d^2)
        
        Args:
            offbit: Input OffBit
            frequency: Resonance frequency in Hz
            distance: Spatial distance for decay calculation
        """
        k = 0.0002  # spatial decay constant
        c = 1.0     # amplitude constant
        
        decay_factor = c * np.exp(-k * distance**2)
        frequency_factor = np.sin(2 * np.pi * frequency * distance) if distance > 0 else 1.0
        
        # Apply resonance to each bit with frequency-dependent modulation
        result_bits = offbit.bits.copy()
        for i in range(24):
            if offbit.bits[i]:
                # Modulate based on bit position and frequency
                phase = 2 * np.pi * frequency * i / 24
                modulation = (1 + np.cos(phase)) / 2
                result_bits[i] = bool(modulation * decay_factor > 0.5)
        
        return OffBit(result_bits, offbit.position)
    
    @staticmethod
    def entanglement_op(b1: OffBit, b2: OffBit, coherence: float = 1.0) -> Tuple[OffBit, OffBit]:
        """
        Entanglement operation: creates correlated OffBit pair
        
        Args:
            b1, b2: Input OffBits
            coherence: Coherence factor (0-1)
        """
        # Create entangled state based on coherence
        correlation_mask = np.random.random(24) < coherence
        
        result1_bits = b1.bits.copy()
        result2_bits = b2.bits.copy()
        
        # Apply correlation where mask is True
        for i in range(24):
            if correlation_mask[i]:
                # Entangled bits have correlated values
                if np.random.random() < 0.5:
                    result1_bits[i] = result2_bits[i] = True
                else:
                    result1_bits[i] = result2_bits[i] = False
        
        return OffBit(result1_bits, b1.position), OffBit(result2_bits, b2.position)
    
    @staticmethod
    def superposition_op(offbits: List[OffBit], weights: List[float]) -> OffBit:
        """
        Superposition operation: weighted combination of states
        
        Args:
            offbits: List of input OffBits
            weights: Corresponding weights (must sum to 1)
        """
        if len(offbits) != len(weights):
            raise ValueError("Number of OffBits must match number of weights")
        
        if abs(sum(weights) - 1.0) > 1e-10:
            raise ValueError("Weights must sum to 1.0")
        
        # Compute weighted average for each bit position
        result_bits = np.zeros(24, dtype=float)
        for offbit, weight in zip(offbits, weights):
            result_bits += weight * offbit.bits.astype(float)
        
        # Convert to boolean based on threshold
        threshold = 0.5
        return OffBit((result_bits > threshold).astype(bool), offbits[0].position)

class GlobalCoherenceInvariant:
    """Implementation of P_GCI calculation"""
    
    def __init__(self, delta_t: float = 0.318309886):
        """
        Initialize GCI with temporal parameter
        
        Args:
            delta_t: Temporal alignment parameter (default aligns with Pi resonance)
        """
        self.delta_t = delta_t
        self.pi_resonance_freq = 3.14159  # Hz
    
    def calculate(self, frequencies: List[float]) -> float:
        """
        Calculate Global Coherence Invariant
        
        Args:
            frequencies: List of active toggle frequencies
            
        Returns:
            P_GCI value
        """
        if not frequencies:
            return 1.0
        
        f_avg = np.mean(frequencies)
        return np.cos(2 * np.pi * f_avg * self.delta_t)

class TGICStructure:
    """Triad Graph Interaction Constraint implementation"""
    
    def __init__(self):
        # Define the 9 pairwise interactions
        self.interactions = [
            ('x', 'y'), ('y', 'x'),  # x-y plane interactions
            ('x', 'z'), ('z', 'x'),  # x-z plane interactions  
            ('y', 'z'), ('z', 'y'),  # y-z plane interactions
            ('x-y', 'z'), ('y-z', 'x'), ('z-x', 'y')  # mixed interactions
        ]
        
        # Map interactions to toggle operations
        self.operation_map = {
            ('x', 'y'): ToggleOperation.RESONANCE,
            ('y', 'x'): ToggleOperation.RESONANCE,
            ('x', 'z'): ToggleOperation.ENTANGLEMENT,
            ('z', 'x'): ToggleOperation.ENTANGLEMENT,
            ('y', 'z'): ToggleOperation.SUPERPOSITION,
            ('z', 'y'): ToggleOperation.SUPERPOSITION,
            ('x-y', 'z'): ToggleOperation.AND,
            ('y-z', 'x'): ToggleOperation.XOR,
            ('z-x', 'y'): ToggleOperation.OR
        }
        
        # Interaction weights (must sum to 1)
        self.weights = {interaction: 1.0/9.0 for interaction in self.interactions}
    
    def get_operation(self, interaction: Tuple[str, str]) -> ToggleOperation:
        """Get toggle operation for given interaction"""
        return self.operation_map.get(interaction, ToggleOperation.AND)
    
    def get_weight(self, interaction: Tuple[str, str]) -> float:
        """Get weight for given interaction"""
        return self.weights.get(interaction, 0.0)

class GLRErrorCorrection:
    """Golay-Leech-Resonance error correction system"""
    
    def __init__(self, max_neighbors: int = 20000):
        self.max_neighbors = max_neighbors
        self.golay_overhead = 0.91  # ~91% overhead for Golay (24,12)
        self.temporal_bins_8bit = 256
        self.temporal_bins_16bit = 65536
        
        # Target frequencies for correction
        self.target_frequencies = [
            3.14159,      # Pi resonance
            14.134725,    # First Riemann zeta zero
            21.022040,    # Second Riemann zeta zero
            36.339691,    # Derived frequency
            4.58e14       # Luminescence frequency
        ]
    
    def correct_frequency(self, measured_freq: float, weights: List[float]) -> float:
        """
        GLR frequency correction algorithm
        
        Args:
            measured_freq: Measured frequency value
            weights: NRCI-based weights for each target frequency
            
        Returns:
            Corrected frequency
        """
        if len(weights) != len(self.target_frequencies):
            weights = [1.0] * len(self.target_frequencies)
        
        # Find closest target frequency weighted by NRCI
        min_error = float('inf')
        corrected_freq = measured_freq
        
        for target_freq, weight in zip(self.target_frequencies, weights):
            weighted_error = weight * abs(measured_freq - target_freq)
            if weighted_error < min_error:
                min_error = weighted_error
                corrected_freq = target_freq
        
        return corrected_freq
    
    def correct_offbit(self, offbit: OffBit, neighbors: List[OffBit]) -> OffBit:
        """
        Apply GLR error correction to an OffBit using neighbor information
        
        Args:
            offbit: OffBit to correct
            neighbors: Neighboring OffBits for spatial correction
            
        Returns:
            Error-corrected OffBit
        """
        # Limit number of neighbors for computational efficiency
        if len(neighbors) > self.max_neighbors:
            neighbors = neighbors[:self.max_neighbors]
        
        corrected_bits = offbit.bits.copy()
        
        # Apply Golay-style error correction
        for bit_idx in range(24):
            # Count neighbor votes for this bit position
            neighbor_votes = sum(1 for neighbor in neighbors if neighbor.bits[bit_idx])
            total_neighbors = len(neighbors)
            
            if total_neighbors > 0:
                # Majority voting with distance weighting
                vote_ratio = neighbor_votes / total_neighbors
                
                # Apply correction if strong consensus disagrees with current bit
                if vote_ratio > 0.7 and not offbit.bits[bit_idx]:
                    corrected_bits[bit_idx] = True
                elif vote_ratio < 0.3 and offbit.bits[bit_idx]:
                    corrected_bits[bit_idx] = False
        
        return OffBit(corrected_bits, offbit.position)

class NonRandomCoherenceIndex:
    """NRCI calculation and monitoring"""
    
    def __init__(self, gci: GlobalCoherenceInvariant):
        self.gci = gci
    
    def calculate(self, toggle_operations: List[Tuple[OffBit, OffBit]], 
                  frequencies: List[float]) -> float:
        """
        Calculate Non-Random Coherence Index
        
        Args:
            toggle_operations: List of (input, output) OffBit pairs
            frequencies: Active frequencies in the system
            
        Returns:
            NRCI value (0-1, target >0.999997)
        """
        if not toggle_operations:
            return 1.0
        
        p_gci = self.gci.calculate(frequencies)
        total_error = 0.0
        
        for input_bit, output_bit in toggle_operations:
            # Calculate ideal output based on P_GCI
            ideal_output = self._calculate_ideal_output(input_bit, p_gci)
            
            # Calculate error between actual and ideal
            error = self._calculate_bit_error(output_bit, ideal_output)
            total_error += error
        
        # NRCI formula: 1 - (sum of errors) / (9 * N_toggles)
        n_toggles = len(toggle_operations)
        nrci = 1.0 - (total_error / (9.0 * n_toggles))
        
        return max(0.0, min(1.0, nrci))  # Clamp to [0,1]
    
    def _calculate_ideal_output(self, input_bit: OffBit, p_gci: float) -> OffBit:
        """Calculate ideal OffBit output based on P_GCI"""
        # Simplified ideal calculation - in practice this would be more complex
        ideal_bits = input_bit.bits.copy()
        
        # Apply P_GCI modulation to each bit
        for i in range(24):
            if input_bit.bits[i]:
                # Modulate based on P_GCI and bit position
                modulation = (1 + p_gci * np.cos(2 * np.pi * i / 24)) / 2
                ideal_bits[i] = modulation > 0.5
        
        return OffBit(ideal_bits, input_bit.position)
    
    def _calculate_bit_error(self, actual: OffBit, ideal: OffBit) -> float:
        """Calculate error between actual and ideal OffBits"""
        # Hamming distance normalized by bit count
        differences = np.sum(actual.bits != ideal.bits)
        return differences / 24.0

class UBPBitfield:
    """Main Bitfield implementation for UBP computations"""
    
    def __init__(self, dimensions: Tuple[int, int, int, int, int, int] = (170, 170, 170, 5, 2, 2)):
        """
        Initialize UBP Bitfield
        
        Args:
            dimensions: 6D dimensions of the Bitfield
        """
        self.dimensions = dimensions
        self.total_cells = np.prod(dimensions)
        
        # Use sparse representation for memory efficiency
        self.offbits: Dict[Tuple[int, int, int, int, int, int], OffBit] = {}
        
        # Initialize core components
        self.toggle_algebra = ToggleAlgebra()
        self.gci = GlobalCoherenceInvariant()
        self.tgic = TGICStructure()
        self.glr = GLRErrorCorrection()
        self.nrci_calculator = NonRandomCoherenceIndex(self.gci)
        
        # Performance tracking
        self.active_frequencies: List[float] = []
        self.toggle_history: List[Tuple[OffBit, OffBit]] = []
    
    def set_offbit(self, position: Tuple[int, int, int, int, int, int], offbit: OffBit):
        """Set OffBit at specified position"""
        if not self._is_valid_position(position):
            raise ValueError(f"Invalid position {position} for dimensions {self.dimensions}")
        
        self.offbits[position] = offbit
    
    def get_offbit(self, position: Tuple[int, int, int, int, int, int]) -> Optional[OffBit]:
        """Get OffBit at specified position"""
        return self.offbits.get(position)
    
    def get_neighbors(self, position: Tuple[int, int, int, int, int, int], 
                     radius: int = 1) -> List[OffBit]:
        """Get neighboring OffBits within specified radius"""
        neighbors = []
        x, y, z, l, m, n = position
        
        for dx in range(-radius, radius + 1):
            for dy in range(-radius, radius + 1):
                for dz in range(-radius, radius + 1):
                    if dx == dy == dz == 0:
                        continue
                    
                    neighbor_pos = (x + dx, y + dy, z + dz, l, m, n)
                    if self._is_valid_position(neighbor_pos):
                        neighbor = self.get_offbit(neighbor_pos)
                        if neighbor is not None:
                            neighbors.append(neighbor)
        
        return neighbors
    
    def apply_toggle_operation(self, op: ToggleOperation, 
                             offbit1: OffBit, 
                             offbit2: Optional[OffBit] = None,
                             **kwargs) -> OffBit:
        """Apply toggle operation to OffBit(s)"""
        if op == ToggleOperation.AND:
            if offbit2 is None:
                raise ValueError("AND operation requires two OffBits")
            result = self.toggle_algebra.and_op(offbit1, offbit2)
        
        elif op == ToggleOperation.XOR:
            if offbit2 is None:
                raise ValueError("XOR operation requires two OffBits")
            result = self.toggle_algebra.xor_op(offbit1, offbit2)
        
        elif op == ToggleOperation.OR:
            if offbit2 is None:
                raise ValueError("OR operation requires two OffBits")
            result = self.toggle_algebra.or_op(offbit1, offbit2)
        
        elif op == ToggleOperation.RESONANCE:
            frequency = kwargs.get('frequency', 3.14159)
            distance = kwargs.get('distance', 0.0)
            result = self.toggle_algebra.resonance_op(offbit1, frequency, distance)
        
        elif op == ToggleOperation.ENTANGLEMENT:
            if offbit2 is None:
                raise ValueError("Entanglement operation requires two OffBits")
            coherence = kwargs.get('coherence', 1.0)
            result1, result2 = self.toggle_algebra.entanglement_op(offbit1, offbit2, coherence)
            # Store both results, return first
            self.set_offbit(offbit2.position, result2)
            result = result1
        
        elif op == ToggleOperation.SUPERPOSITION:
            offbits = kwargs.get('offbits', [offbit1])
            weights = kwargs.get('weights', [1.0])
            result = self.toggle_algebra.superposition_op(offbits, weights)
        
        else:
            raise ValueError(f"Unknown toggle operation: {op}")
        
        # Record operation for NRCI calculation
        self.toggle_history.append((offbit1, result))
        
        return result
    
    def calculate_nrci(self) -> float:
        """Calculate current NRCI for the Bitfield"""
        return self.nrci_calculator.calculate(self.toggle_history, self.active_frequencies)
    
    def apply_glr_correction(self):
        """Apply GLR error correction to all OffBits"""
        corrected_offbits = {}
        
        for position, offbit in self.offbits.items():
            neighbors = self.get_neighbors(position, radius=2)
            corrected = self.glr.correct_offbit(offbit, neighbors)
            corrected_offbits[position] = corrected
        
        # Update all OffBits with corrected versions
        self.offbits.update(corrected_offbits)
    
    def _is_valid_position(self, position: Tuple[int, int, int, int, int, int]) -> bool:
        """Check if position is within Bitfield dimensions"""
        return all(0 <= pos < dim for pos, dim in zip(position, self.dimensions))
    
    def get_statistics(self) -> Dict[str, Union[int, float]]:
        """Get Bitfield statistics"""
        return {
            'total_cells': self.total_cells,
            'active_offbits': len(self.offbits),
            'occupancy_ratio': len(self.offbits) / self.total_cells,
            'current_nrci': self.calculate_nrci(),
            'active_frequencies': len(self.active_frequencies),
            'toggle_operations': len(self.toggle_history)
        }

# Example usage and validation functions
def create_sample_bitfield() -> UBPBitfield:
    """Create a sample Bitfield for testing"""
    bitfield = UBPBitfield()
    
    # Add some sample OffBits
    for i in range(10):
        position = (i, i, i, 0, 0, 0)
        bits = np.random.choice([True, False], size=24)
        offbit = OffBit(bits, position)
        bitfield.set_offbit(position, offbit)
    
    return bitfield

def validate_nrci_target() -> bool:
    """Validate that NRCI can achieve target >99.9997%"""
    bitfield = create_sample_bitfield()
    
    # Perform some toggle operations
    for position, offbit in list(bitfield.offbits.items())[:5]:
        neighbors = bitfield.get_neighbors(position)
        if neighbors:
            result = bitfield.apply_toggle_operation(
                ToggleOperation.RESONANCE, 
                offbit, 
                frequency=14.134725
            )
            bitfield.set_offbit(position, result)
    
    # Apply GLR correction
    bitfield.apply_glr_correction()
    
    # Check NRCI
    nrci = bitfield.calculate_nrci()
    target_nrci = 0.999997
    
    print(f"Achieved NRCI: {nrci:.6f}")
    print(f"Target NRCI: {target_nrci:.6f}")
    print(f"Target met: {nrci >= target_nrci}")
    
    return nrci >= target_nrci

if __name__ == "__main__":
    # Run validation
    print("UBP Mathematical Framework Implementation")
    print("=" * 50)
    
    # Test basic functionality
    bitfield = create_sample_bitfield()
    stats = bitfield.get_statistics()
    
    print("Bitfield Statistics:")
    for key, value in stats.items():
        print(f"  {key}: {value}")
    
    print("\nValidating NRCI target...")
    validate_nrci_target()